Find the gradient of the curve x^2 + 2xy-2y^2 +x=2 at the point (-4,1)

Question

anonymous · Answer

First, you find out partial x and partial y.. do you have that yet?

fibonaccichick666 · Answer

I'd suggest starting with what is a gradient then go into partial derivatives

anonymous · Answer

Does this help?$$
x^2~+~2xy~-~2y^2~+x~=2 \
2x+2\frac{\textrm{d}y}{\textrm{d}x}-4\frac{\textrm{d}y}{\textrm{d}x}+1~=~0
$$I can't remember if gradient is the same thing as slope.

amistre64 · Answer

gradient means slope in certain context yes; its also a term used to find the normal to a surface

amistre64 · Answer

i think you missed your product rule tho

amistre64 · Answer

$$x^2~+~2xy~-~2y^2~+x~=2 $$
$$2xx'~+~2x'y+~2xy'~-~4yy'~+x'~=0 $$
if "wrt.x" then x' = dx/dx = 1
$$2x~+~2y+~2xy'~-~4yy'~+1~=0 $$

amistre64 · Answer

plug in (-4,1) and solve for y'